Abstract

A side-coupled spaced sequence of resonators (SCSSOR) displays strong dispersion with a magnitude much larger than that of conventional waveguides. We investigate the Sagnac effect in a SCSSOR structure. An explicit expression of the Sagnac phase difference of the structure is derived and discussed. The results show the sensitivity is proportional to the number and dispersion intensity of resonators. Compared with other resonator structures, one advantage is that it is not necessary to preserve the same circumference of each resonator, which is difficult to realize in practice. The results also predict a SCSSOR structure can be used for the realization of highly sensitive and compact integrated rotation sensors and gyroscopes.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]

2010

2009

2008

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

2007

2006

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96(5), 053901 (2006).
[CrossRef] [PubMed]

2005

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056621 (2005).
[CrossRef] [PubMed]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

S. Mookherjea, “Dispersion characteristics of coupled-resonator optical waveguides,” Opt. Lett. 30(18), 2406–2408 (2005).
[CrossRef] [PubMed]

2004

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12(1), 90–103 (2004).
[CrossRef] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

2003

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

2002

J. E Heebner, R. W. Boyd, and Q. H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(3 Pt 2B), 036619 (2002).
[CrossRef] [PubMed]

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19(4), 722–731 (2002).
[CrossRef]

2000

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

1999

1967

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
[CrossRef]

Boag, A.

Boyd, R. W.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

J. E Heebner, R. W. Boyd, and Q. H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(3 Pt 2B), 036619 (2002).
[CrossRef] [PubMed]

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19(4), 722–731 (2002).
[CrossRef]

Chang, H.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

E Heebner, J.

J. E Heebner, R. W. Boyd, and Q. H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(3 Pt 2B), 036619 (2002).
[CrossRef] [PubMed]

Farca, G.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

Hah, D.

Heebner, J. E.

Huang, Y.

Khurgin, J. B.

Lee, R. K.

Li, Z.

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Mookherjea, S.

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Naweed, A.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Paloczi, G. T.

Park, Q. H.

J. E Heebner, R. W. Boyd, and Q. H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(3 Pt 2B), 036619 (2002).
[CrossRef] [PubMed]

Park, Q.-H.

Peng, C.

Poon, J. K. S.

Post, E. J.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
[CrossRef]

Qiu, W.

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Rosenberger, A. T.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

Scherer, A.

Scheuer, J.

Shopova, S. I.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

Steinberg, B. Z.

Tian, H.

Y. Zhang, H. Tian, X. Zhang, N. Wang, J. Zhang, H. Wu, and P. Yuan, “Experimental evidence of enhanced rotation sensing in a slow-light structure,” Opt. Lett. 35(5), 691–693 (2010).
[CrossRef] [PubMed]

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Wang, H.

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Wang, J.

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Wang, N.

Y. Zhang, H. Tian, X. Zhang, N. Wang, J. Zhang, H. Wu, and P. Yuan, “Experimental evidence of enhanced rotation sensing in a slow-light structure,” Opt. Lett. 35(5), 691–693 (2010).
[CrossRef] [PubMed]

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Wu, H.

Xu, A.

Xu, Y.

Yariv, A.

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96(5), 053901 (2006).
[CrossRef] [PubMed]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12(1), 90–103 (2004).
[CrossRef] [PubMed]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[CrossRef]

Yuan, P.

Y. Zhang, H. Tian, X. Zhang, N. Wang, J. Zhang, H. Wu, and P. Yuan, “Experimental evidence of enhanced rotation sensing in a slow-light structure,” Opt. Lett. 35(5), 691–693 (2010).
[CrossRef] [PubMed]

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Zhang, D.

Zhang, J.

Zhang, X.

Zhang, Y.

Y. Zhang, H. Tian, X. Zhang, N. Wang, J. Zhang, H. Wu, and P. Yuan, “Experimental evidence of enhanced rotation sensing in a slow-light structure,” Opt. Lett. 35(5), 691–693 (2010).
[CrossRef] [PubMed]

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Appl. Opt.

Electron. Lett.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Phys. Lett. A

Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372(36), 5848–5852 (2008).
[CrossRef]

Phys. Rev. A

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[CrossRef]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

J. E Heebner, R. W. Boyd, and Q. H. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(3 Pt 2B), 036619 (2002).
[CrossRef] [PubMed]

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056621 (2005).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96(5), 053901 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of a side-coupled spaced sequence of resonators. E 1 is the incident field, E 4 is the field injected into the resonator, E 3 is the field after one pass around the resonator, E 2 is the transmitted field.

Fig. 2
Fig. 2

Dependence of phase difference on rotary velocity and frequency in a resonator: ne = 1.5, R = 0.12m, N = 20, and t 2 = 0.6.

Fig. 3
Fig. 3

Experiment setup for measurement of the phase difference introduced by rotation in a SCSSOR structure: M = 2, ne = 1.5, R = 0.12m, N = 20, and t 2 = 0.6. PC, polarization controller.

Fig. 4
Fig. 4

(a) Experimental interference spectrum of the SCSSOR structure at the rotary velocity of 2 π r a d / s . (b) Experimental interference spectra of one resonator at different rotary velocities: 0, 0.5 π r a d / s , π r a d / s , 1.5 π r a d / s , and 2 π r a d / s .

Fig. 5
Fig. 5

Theoretical and experimental phase difference at the resonance frequency versus rotary velocity. The rotary velocity is from 0 to 2 π r a d / s and is in an increasing step of π / 6 r a d / s in the experimental result.

Fig. 6
Fig. 6

A compact SCSSOR structure.

Fig. 7
Fig. 7

ng /ne at resonance frequency versus t (ne = 3.42, R = 10 μm ).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

[ E 4 E 2 ] = [ t i k i k t ] [ E 3 E 1 ] ,
E 3 = e i ϕ E 4 .
E 2 = E 1 exp ( i Φ ) ,
Δ ϕ ( ω , Ω ) = N 4 ω A c 2 Ω ,
d Φ = Φ / ω ϕ / ω d ϕ = n g n e d ϕ .
Δ Φ ( ω , Ω ) = 2 | ϕ ( ω , 0 ) ϕ ( ω , Ω ) n g n e d ϕ | .
Δ Φ t ( ω , Ω ) = 2 j = 1 M Δ Φ j ( ω , Ω ) = 2 j = 1 M | ϕ ( ω , 0 ) ϕ ( ω , Ω ) n g , j n e d ϕ | ,
I o u t ( ω , Ω ) = I i n sin 2 ( Δ Φ t ( ω , Ω ) / 2 ) .

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